Advertisements
Advertisements
Question
Consider the situation shown in the following figure All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.
Advertisements
Solution
Mass of each block is 1 kg, \[\sin \theta_1 = \frac{4}{5}\]
\[\sin \theta_2 = \frac{3}{5}\]
The free-body diagrams for both the boxes are shown below:
mgsinθ1 − T = ma ...(i)
T − mgsinθ2 = ma ...(ii)
Adding equations (i) and (ii),we get:
mg(sinθ1 − sinθ2) = 2ma
⇒ 2a = g (sinθ1 − sinθ2)
\[\Rightarrow a = \frac{g}{5} \times \frac{1}{2}\]
\[ = \frac{g}{10}\]
APPEARS IN
RELATED QUESTIONS
A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)
A monkey of mass 40 kg climbs on a rope in given Figure which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey
(a) climbs up with an acceleration of 6 m s–2
(b) climbs down with an acceleration of 4 m s–2
(c) climbs up with a uniform speed of 5 m s–1
(d) falls down the rope nearly freely under gravity?
(Ignore the mass of the rope).
You are travelling in a car. The driver suddenly applies the brakes and you are pushed forward. Why does this happen?
Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than that of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.
Two blocks A and B of mass mA and mB , respectively, are kept in contact on a frictionless table. The experimenter pushes block A from behind, so that the blocks accelerate. If block A exerts force F on block B, what is the force exerted by the experimenter on block A?
Both the springs shown in the following figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?
A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the following figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth h.
A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg, respectively. Assuming that the magnitudes of acceleration and deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 m/s2.
The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall to the earth's surface with a constant velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v?
Find the acceleration of the block of mass M in the situation shown in the following figure. All the surfaces are frictionless and the pulleys and the string are light.
A block A can slide on a frictionless incline of angle θ and length l, kept inside an elevator going up with uniform velocity v in the following figure. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.
A body of mass m moving with a velocity v is acted upon by a force. Write an expression for change in momentum in each of the following cases: (i) When v << c, (ii) When v → c and (iii) When v << c but m does not remain constant. Here, c is the speed of light.
A body of mass 200 g is moving with a velocity of 5 ms−1. If the velocity of the body changes to 17 ms−1, calculate the change in linear momentum of the body.
What do you understand by the term momentum?
Name the physical quantity which equals the rate of change of linear momentum.
A ball is thrown upward and reaches a maximum height of 19.6 m. Find its initial speed?
What do you mean by the conservation of momentum? Briefly, explain the collision between two bodies and the conservation of momentum.
A cricket ball of mass 150 g has an initial velocity `u = (3hati + 4hatj)` m s−1 and a final velocity `v = - (3hati + 4hatj)` m s−1 after being hit. The change in momentum (final momentum-initial momentum) is (in kg m s1)
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
Why is catching a slow-moving ball easier than catching a fast-moving ball?
